1. Gases
HW: read CH 13

2. The Nature of Gases Gases occupy the entire volume available
11 elements may be found as a gas (He, F2, etc.) 
Other elements may combine with the 11 elements to make gases as well (CO2, CH4, etc.) 

3. Physical properties of all gases
Gases have mass (empty basketball vs. full basketball) and density
It is easy to compress gases (unlike solids and liquids)
No definite shape or volume but will expand to fill as much space as possible
Gas particles diffuse completely in each other, which indicates the particles are moving
Gases exert pressure
Pressure of a gas depends on its temperature

4. Pressure The only time there is a lack of pressure is in a vacuum
The air around us exerts atmospheric pressure (atm). This is because air has a mass and gravity acts on air.
Atm varies with how much water vapor is present in the air
1. Water vapor is lighter than air
2. High water vapor results in a low atm
3. Thus, a low atm indicates a high likelihood of rain

5. *Atmospheric pressure is measured with barometers
Basically, a barometer is a dish filled with Mercury (Hg) and a tube put vertically in the reservoir upside down.
The mercury moves up the tube to a height so that the pressure on the reservoir of mercury equals the pressure from the column of mercury
The column of mercury will fill with 760 millimeters with the pressure of 1 atmosphere at sea level

6. Conversions
1.00 atm = 760. mmHg = 760. torr = kPa = 101,325 Pa = psi
A) 657 mmHg = _____ atm
B) 830 torr = _____ atm
C) 28 psi = _____ pascals

7. Kinetic Molecular Theory
Kinetic energy is the energy of motion
Kinetic Theory: The tiny particles in all forms of matter are in constant motion.
Basis for many gas laws
NOTE: all gas calculations use Kelvin for temperature

8. Gas Laws There are 4 variables when measuring gases
Pressure: P – atm, torr, Kpa, or mm Hg
Volume: V – L or mL
Temperature: T – MUST be in Kelvins (K)
Moles: n – mol
When you see STP that means Standard Temperature and Pressure = 273 K and 1 atm (or 760 mmHg)

9. Pressure and Volume – Boyle’s Law
Boyle trapped a fixed amount of air in a tube
He then changed the pressure and measured the change in volume
Determined the pressure and volume of a sample of gas at constant temperature are inversely proportional to each other
P1V1 = P2V2

10. Pressure and Volume – Boyle’s Law
P1V1 = P2V2
EXAMPLE: A gas occupies a volume of 2.45 L at a pressure of 1.03 atm and temperature of 293 K. What volume will the gas occupy if the pressure changes to atm and the temperature remains unchanged?
(1.03 atm)(2.45 L) = (0.980)(V2)
2.58 = V2

11. Pressure and Volume – Boyle’s Law
YOU TRY!
A) If a 1.23 L sample of a gas at 53.0 torr is put under pressure up to a value of 240. torr at a constant temperature, what is the new volume?
B) In a specific automobile engine the initial cylinder volume is L. After the piston moves up, the volume is 0.075L. The fuel-air mixture initially has a pressure of 1.00atm. Calculate the pressure of the compressed fuel-air mixture.

12. Temperature and Volume – Charles’s Law
Charles put a fixed amount of a gas in a container that had a movable top
He then put this container in a water bath and measured the distance the top moved (measured change in volume)
Determined that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature
V1T2 = V2T1
(temp MUST be in Kelvin)

13. Temperature and Volume – Charles’s Law
V1T2 = V2T1 (temp MUST be in Kelvin)
EXAMPLE: What will be the volume of a gas sample at 355 K if its volume at 273 K is 8.57 L? Assume pressure remains constant.
(8.57 L)(355 K) = (V2)(273 K)
11.1 L = V2

14. Temperature and Volume – Charles’s Law
YOU TRY!
A) A gas sample at 83oC occupies a volume of 1400m3. At what temp will it occupy 1200m3? Answer in oC. Hint: K = oC
B) An 11.0 L sample of a gas is collected at 276 K and then cooled by 14 K. The pressure is held constant at atm. Calculate the new volume of the gas.

15. Volume and Moles: Avogadro’s Law
Avogadro’s Law states that, at constant temperature and pressure, volume is directly proportional to the number of moles of gas present. This means the volume of a gas increases with increasing number of moles and vice versa.
V1 = V2
n1 n2

16. Volume and Moles: Avogadro’s Law
V1 = V2
n1 n2
EXAMPLE: Sample 1 of nitrogen gas contains 1.5 mol of N2 and has a volume of 36.7 L at 25oC and 1 atm. Sample 2 has a volume of 16.5 L at 25oC and 1 atm. Calculate the number of moles of N2 in Sample 2.
36.7L = 16.5L n2 = 0.67 mol
1.5 mol n2

17. Volume and Moles: Avogadro’s Law
YOU TRY!
A) If mol of argon gas occupies a volume of 652 mL at a particular temp and pressure, what volume would mol of argon occupy under the same condition?
B) If 2.11 g of Neon gas occupies a volume of 12.0 L at oC. What volume will 6.58 g of Neon occupy under the same conditions? (hint- convert to moles)

18. Pressure and Temperature: Gay-Lussac’s Law
At constant volume, pressure is directly proportional to temperature. This means that temperature increases with increasing pressure and vice versa.
P1 = P2
T1 T2

19. Pressure and Temperature: Gay-Lussac’s Law
P1 = P2
T1 T2
EXAMPLE: A gas at 25.0oC in a closed container has its pressured raised from 150. atm to 160. atm. What is the final temperature of the gas?
150atm = 160 atm T2 = 26.7oC
25oC T2

20. Pressure and Temperature: Gay-Lussac’s Law
YOU TRY!
A) A gas exerts a pressure of 900 mmHg at 20oC. What temperature would be required to lower the pressure to 1.00 atm?
B) A gas at 20oC in a closed container has its pressured raised from 125. atm to 140. atm. What is the final temperature of the gas in Kelvin?

21. The Combined Gas Law
Yikes! Do you really need to learn all these separate laws?? NO!! They can all go together in 1 law to memorize. If any variable stays constant it will cancel out.
P1V1 = P2V2
n1T1 n2T2
(9 min crash course)

22. Ideal Gas Law
If you put all the gas laws together, the Ideal Gas Law is created
PV = nRT
R = universal gas constant
= L atm K-1 mol-1
(P= pressure in atm; V= volume in L; n= number moles; T= temp in Kelvin)

23. PV = nRT
EXAMPLE: Assuming ideal behavior, how many moles of Helium gas are in a sample that has a volume of L at a temperature of 0.00 oC and a pressure of atm?
P = 1.20 atm; V = 8.12 L; n = x; R= ; T = 0oC = 273 K
(1.20)(8.12)=x( )(273)
x = mol He

24. YOU TRY!!
A) A weather balloon contains 1.10 x 105 mol of helium and has a volume of 2.70 x 106 L at 1.00 atm pressure. Calculate the temperature of the helium in the balloon in Kelvins and in Celsius degrees.
B) A sample of aluminum chloride weighing g was vaporized at 350. oC and 1.00 atm pressure to produce mL of vapor. Calculate a value for the Molar Mass of aluminum chloride.

25. Can you figure out which formula to use?
C) A sample of argon gas with a volume of 11.0 L at a temperature of 13oC and a pressure of atm is heated to 56oC and a pressure of 1.18 atm. Calculate the final volume

26. Dalton’s Law of Partial Pressures
For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present.
The partial pressure of a gas is the pressure that the gas would exert if it were alone in the container.
Ptotal = P1 + P2 + P3 etc
Ptotal = ntotal (RT/V)

27. Dalton’s Law of Partial Pressures
Ptotal = P1 + P2 + P3 etc Ptotal = ntotal (RT/V)
EXAMPLE: A 2.0 L flask contains a mixture of nitrogen gas and oxygen gas at 25oC. The total pressure of the gaseous mixture is atm, and the mixture is known to contain mol N2. Calculate the partial pressure of oxygen and the moles of oxygen present.
Ptotal = 0.91 atm; V = 2.0 L; N2 n = mol; T = 298 K; R = ; O2 n = ? (need total);
ntotal = PtotalV ntotal = 0.91(2.0) ntotal = mol
RT ( )(298)
0.074 mol – mol = mol O2
PO2 = (0.024)( )(298)/2.0 PO2 = 0.29 atm

28. Dalton’s Law of Partial Pressures
YOU TRY! If 5.0 g of nitrogen gas and 5.0 g of chlorine gas are injected in to a 2.0 L vessel at a temperature of 65 oC, what will the partial pressure of each gas be? What will the total pressure in the container be?
P N2 = 2.5 atm
P Cl2 = 0.98 atm
Total = 3.48 atm

29. Gas Stoichiometry Lots of “fun” calculations can be determined
One mole of any ideal gas at standard temperature and pressure (STP) will occupy a volume of 22.4 L (standard temp = 298K/25oC, standard pressure = atm)

30. Gas Stoichiometry
Example: Calculate the volume of carbon dioxide gas produced when 9.85 g of barium carbonate is completely decomposed in the reaction below at STP.
BaCO3(s)BaO(s) +CO2(g)
P=1.00atm; V=?; n=figure it out; R= ; T=298K
9.85gBaCO3 x 1 mol = mol BaCO3 x 1 mol CO2 = .0499mol CO2
g mol BaCO3
V = (0.499)( )(298) / 1 = 1.22 L

31. Gas Stoichiometry
YOU TRY! Ammonia is commonly used as a fertilizer to provide a source of nitrogen for plants. A sample of NH3 occupies 5.00 L at 25oC and 15.0 atm. What volume will this occupy at STP? (hint 1 mol = 22.4 L)
n= PV/RT; n = (15x5)/(.08206)(298)= 3.07 mol NH3
3.07 mol NH3 x (22.4L/1mol) = 68.8L